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Primal or dual strong-duality in nonconvex optimization and a class of quasiconvex problems having zero duality gap

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Abstract

Primal or dual strong-duality (or min-sup, inf-max duality) in nonconvex optimization is revisited in view of recent literature on the subject, establishing, in particular, new characterizations for the second case. This gives rise to a new class of quasiconvex problems having zero duality gap or closedness of images of vector mappings associated to those problems. Such conditions are described for the classes of linear fractional functions and that of quadratic ones. In addition, some applications to nonconvex quadratic optimization problems under a single inequality or equality constraint, are presented, providing new results for the fulfillment of zero duality gap or dual strong-duality.

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Acknowledgements

The research for the first author was supported by the Programa Nacional de Innovación para la Competitividad y Productividad (Innóvate Perú), under contract 013-INNOVATEPERU-ECIP-2016, and was carried out partially while he was visiting IMCA-UNI during 2016. He is grateful for the hospitality of its members. The research material of this work was also supported in part by FONDECYT 115-0973 (Chile) and Basal project, CMM, Universidad de Chile, for the first author; whereas the fourth author was supported by FONDECYT 182-2015 (Perú), and part of his research was carried out while visited University of Concepcion. The authors want to express their gratitude to the referee for his/her careful reading of the manuscript and criticism, which were taken into account in the present version.

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Authors and Affiliations

  1. Departamento de Ingeniería Matemática, Universidad de Concepción, Concepción, Chile

    Fabián Flores-Bazán

  2. IMCA, Facultad de Ciencias, Universidad Nacional de Ingeniería, Lima, Peru

    William Echegaray & Eladio Ocaña

  3. Departamento de Matemáticas, Facultad de Ciencias, Universidad del Bío Bío, Concepción, Chile

    Fernando Flores-Bazán

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  1. Fabián Flores-Bazán
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  2. William Echegaray
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  3. Fernando Flores-Bazán
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  4. Eladio Ocaña
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Correspondence to Fabián Flores-Bazán.

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Flores-Bazán, F., Echegaray, W., Flores-Bazán, F. et al. Primal or dual strong-duality in nonconvex optimization and a class of quasiconvex problems having zero duality gap. J Glob Optim 69, 823–845 (2017). https://doi.org/10.1007/s10898-017-0542-9

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  • DOI: https://doi.org/10.1007/s10898-017-0542-9

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